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International competition SRMC 2003 P-4

Source:

September 8, 2010
algebra proposedalgebra

Problem Statement

Find ∑k∈A1k−1 \sum_{k \in A} \frac{1}{k-1} where A={mn:m,n∈Zm,n≥2}A= \{ m^n : m,n \in \mathbb{Z} m,n \geq 2 \} .
Problem was post earlier [url=http://www.artofproblemsolving.com/Forum/viewtopic.php?f=67&t=29456&hilit=silk+road]here , but solution not gives and olympiad doesn't indicate, so I post it again :blush:
Official solution [url=http://www.artofproblemsolving.com/Forum/viewtopic.php?f=125&t=365714&p=2011659#p2011659]here
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